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1
JEE Main 2021 (Online) 25th July Morning Shift
Numerical
+4
-1
Let $$S = \left\{ {n \in N\left| {{{\left( {\matrix{ 0 & i \cr 1 & 0 \cr } } \right)}^n}\left( {\matrix{ a & b \cr c & d \cr } } \right) = \left( {\matrix{ a & b \cr c & d \cr } } \right)\forall a,b,c,d \in R} \right.} \right\}$$, where i = $$\sqrt { - 1}$$. Then the number of 2-digit numbers in the set S is _____________.
2
JEE Main 2021 (Online) 18th March Morning Shift
Numerical
+4
-1
Let z1, z2 be the roots of the equation z2 + az + 12 = 0 and z1, z2 form an equilateral triangle with origin. Then, the value of |a| is
3
JEE Main 2021 (Online) 16th March Morning Shift
Numerical
+4
-1
Let z and $$\omega$$ be two complex numbers such that $$\omega = z\overline z - 2z + 2,\left| {{{z + i} \over {z - 3i}}} \right| = 1$$ and Re($$\omega$$) has minimum value. Then, the minimum value of n $$\in$$ N for which $$\omega$$n is real, is equal to ______________.
| z + 5 | $$\le$$ 4 and z(1 + i) + $$\overline z$$(1 $$-$$ i) $$\ge$$ $$-$$10, i = $$\sqrt { - 1}$$.
If the maximum value of | z + 1 |2 is $$\alpha$$ + $$\beta$$$$\sqrt 2$$, then the value of ($$\alpha$$ + $$\beta$$) is ____________.